1. Field of the Invention
The present invention relates to an optical fiber having a high sensitivity to acceleration and a low sensitivity to pressure, for use in a fiber optic accelerometer sensor which detects acceleration. More specifically, the present invention relates to the various concentric layers of an optical fiber having a high sensitivity to acceleration and a low sensitivity to pressure, and to a sensor which uses the fiber.
2. Description of the Related Art
Spatially averaging accelerometer sensors detect acceleration and have many practical uses. For example, spatially averaging accelerometer sensors are used in structural acoustic applications, seismometer applications and structural mechanic applications.
There are many uses for spatially averaging accelerometer sensors in structural acoustic applications. For example, spatially averaging accelerometer sensors can be used to measure structural vibrations leading to sound scattering and radiation which is uncontaminated by higher way number noise. Thus, spatially averaging accelerometer sensors have widespread applications in active sound control to detect aircraft interior noise, underwater vehicle sound radiation/scattering. Moreover, spatially averaging accelerometer sensors can be used in acoustic listening arrays mounted to aircraft and underwater vehicles. Spatially averaging accelerometer sensors can also be used to detect acoustic energy through acceleration, rather than through pressure. In conjunction with a large area pressure sensor, spatially averaging accelerometer sensors would provide a powerful capability for the measurement of acoustic fields near structures having general impedance properties, (e.g. the detection of the acoustic field with high signal to noise even near a soft pressure release boundary).
When used in a seismometer, a spatially averaging accelerometer sensor can be used as a sensing arm of the seismometer. The sensing .arm can be on or under the ground in any desired shape and length, and the acceleration due to a seismic wave can be detected down to very low frequencies.
When used in structural mechanic applications, spatially averaging accelerometer sensors can be used to detect and monitor the vibration level of large scale objects in a noisy environment. Such objects can include large machineries, bridges, buildings, and airplane wings.
Conventional spatially averaging accelerometer sensors typically use piezo electric transducers (PZTs). Unfortunately, spatially averaging accelerometer sensors experience many problems from the use of PZTs. For example, PZTs used in spatially averaging accelerometer sensors typically have a high pressure sensitivity. This high pressure sensitivity causes problems in accurately detecting acceleration. Therefore, in order for the PZTs to accurately detect acceleration, the pressure sensitivity of the PZTs is reduced by enclosing the PZTs in undesirable, heavy metal cases.
Moreover, PZTs cannot be easily conformed to the particular shape required for specific applications, especially when acceleration must be integrated over a large area. In this case, many smaller PZTs must be connected together to form an array of sensors. Unfortunately, an array of sensors is too heavy, especially for many underwater applications where weight is important; and also it is very expensive. Further, an array of sensors is subject to electromagnetic interference since the output signal produced by the array is an electrical signal. Also, an array of sensors is limited to a relatively small size since a large array would be too fragile. Moreover, an array of sensors has an acceleration sensitivity which is undesirably limited at low frequencies.
In view of the problems encountered with using PZTs in spatially averaging accelerometer sensors, it would be desirable to create a spatially averaging accelerometer sensor which uses an optical fiber to detect acceleration, if such a spatially averaging accelerometer sensor could take advantage of the unique capabilities of fiber optic technology.
If a spatially averaging accelerometer sensor used a conventional optical fiber, most applications would require that acceleration be integrated over a defined area and detected down to low frequencies. Therefore, the optical fiber would have to be highly sensitive to acceleration, but be minimally sensitive to pressure. Unfortunately, a conventional optical fiber will not provide both a high sensitivity to acceleration and a low sensitivity to pressure. Therefore, conventional spatially averaging accelerometer sensors do not use optical fibers.
The following is an analysis of a conventional optical fiber to indicate reasons why a conventional optical fiber will not provide the required high sensitivity to acceleration and low sensitivity to pressure.
FIG. 1 is a diagram illustrating a conventional optical fiber which is commercially available. Referring now to FIG. 1, the optical fiber 30 has a center portion 32 which includes a core 33 and a glass cladding 35 which concentrically surrounds the core 33. The cladding 35 has a refractive index slightly less than the refractive index of the core 33, so that light propagates in the core 33 via total internal reflection. The center portion 32 can also includes a glass substrate 37 which concentrically surrounds the cladding 35. A first protecting layer 34 concentrically surrounds the center portion 32. The first protecting layer 34 is usually an ultraviolet (U.V.) curable polymer layer, similar to silicone. A second protecting layer 36 concentrically surrounds the center portion 32 and the first protecting layer 34. The second protecting layer 36 is a hard plastic layer, such as Hytrel (trademark), and is directly adjacent to the first protecting layer 34 with no other layers therebetween. As illustrated in FIG. 1, the center portion 32 has an outside diameter (OD) of about 125 .mu.m, and the first protecting layer 34 has an outside diameter of about 250 .mu.m. Fiber 30 is a typical single-mode conventional fiber.
FIG. 2 is a diagram illustrating a conventional fiber interferometer 38 which can be used to measure the sensitivity of a fiber by measuring the change of the phase of light transmitted through the fiber. Referring now to FIG. 2, the fiber interferometer 38 has a reference arm 40 and a sensing arm 42. The reference arm 40 and the sensing arm 42 are optical fibers. A light source 44 transmits light into an input lead 46. A first coupler 48 couples the input lead 46 to the reference arm 40 and the sensing arm 42, so that light transmitted from the light source 44 is divided and passes through the reference arm 40 and the sensing arm 42. A second coupler 50 couples the reference arm 40 and the sensing arm 42 to an output lead 52, so that light transmitted through the reference arm 40 and the sensing arm 42 is coupled together to the output lead 52. The input lead 46 and the output lead 52 are optical fibers. A detector 54 is connected to the output lead 52. The detector 54 detects changes in the phase of light transmitted from the light source 44, through the reference arm 40 and the sensing arm 42, and then coupled to the output lead 52. The sensitivity of the sensing arm 42 to any field (such as pressure) can then be determined in a conventional manner from the detected phases.
Pressure Sensitivity of Free Fibers
A free fiber is a fiber which is not embedded or encased in an encapsulant. Using the fiber interferometer 38 illustrated in FIG. 2, the pressure sensitivity of the optical phase in a free fiber, such as fiber 30, can be detected. The pressure sensitivity is defined as ##EQU1## where .DELTA..PHI. is the shift in the phase .PHI. due to a pressure change .DELTA.P. If the given pressure change .DELTA..PHI. results in a fiber core axial strain e.sub.Z and radial strain e.sub.r, then the following Equation 1 applies: ##EQU2## where P.sub.11 and P.sub.12 are the elastooptic coefficients of the core and n is the refractive index of the core. Hereinafter, e.sub.z.sup.1 refers to the first term in Equation 1, above. e.sub.r.sup.P and e.sub.z.sup.P refer to the last two terms, respectively, in Equation 1.
FIG. 3 is a diagram illustrating the effects of e.sub.z.sup.1, e.sub.r.sup.P and e.sub.z.sup.P on an optical fiber 30. As illustrated in FIG. 3, e.sub.z.sup.1 results in end pressure which shortens the fiber 30, e.sub.r.sup.P results in lateral pressure which reduces the diameter of the fiber 30, and e.sub.z.sup.P results in lateral pressure which elongates the fiber 30.
FIG. 4 is a graph illustrating the pressure sensitivity of a free fiber 30 (see FIG. 1) as a function of the thickness of the second protecting layer 36, where the second protecting layer 36 is made of the hard plastic material Hytrel (trademark). The thickness of the second protecting layer 36 usually varies in different fibers.
As illustrated in FIG. 4, the largest magnitude contribution is from the term e.sub.z.sup.1, which is the part of ##EQU3## due to the fiber length change. The e.sub.r.sup.P and e.sub.z.sup.P terms are due to the photoelastic effect, and they are opposite in polarity to each other and produce smaller contributions to the magnitude of pressure sensitivity than the term e.sub.z.sup.1. As the thickness of the second protecting layer 36 increases (see FIG. 4), the magnitude of the pressure sensitivity increases rapidly. This rapid increase in magnitude is primarily due to the change in the contribution from the term e.sub.z.sup.1. This pressure sensitivity illustrated in FIG. 4 for a conventional free fiber is too high for use in a spatially averaging accelerometer sensor.
In general, the pressure sensitivity is a very strong function of the elastic moduli of the material (for example, the hard plastic material Hytrel (trademark)) forming the second protecting layer 36 of the fiber 30. For a typical fiber 30, high pressure sensitivity requires a second protecting layer 36 having a low Bulk Modulus and a high Young's Modulus. In this case, the Bulk Modulus determines the "maximum" fiber dimensional changes, while the Young's Modulus governs the fraction of these changes, or strains, which can couple to the center portion 32 (including the core 33) of the fiber.
Pressure Sensitivity of Embedded Fibers
FIG. 5 is a diagram of a planar sensor 58 which uses the conventional fiber 30 illustrated in FIG. 1. FIG. 6 is a cross-section along lines VI--VI in FIG. 5, although not drawn to scale. For example, FIG. 6 shows less optical fiber cross-sections of fiber 30 then would actually be present from a more accurate cross-section of sensor 58. To be used in a spatially averaging accelerometer sensor, the sensor 58 should be capable of functioning as a sensing arm of the accelerometer to detect acceleration. As can be seen from FIGS. 5 and 6, the sensor 58 is formed by a spirally arranged fiber 30, where the spiral is arranged in a single plane. This fiber configuration can be referred to as a "pancaked spiral" configuration. The spirally arranged fiber 30 is embedded in a polyurethane layer 60 (for example, Polyurethane, Uralite 3140 (Trademark)), where polyurethane is a known elastomeric material. To analyze the sensor 58, the polyurethane layer 60 is approximated as a concentric circular coating over the fiber 30, as illustrated in FIG. 7. The approximation illustrated in FIG. 7 is equivalent to assuming that the sensor 58 was formed by spiraling fiber that had first been coated with a concentrically surrounding layer of polyurethane.
FIG. 8 is a graph illustrating the pressure sensitivity of the fiber 30 illustrated in FIG. 7, versus the fiber radius, considering each of the fiber layers. As illustrated in FIG. 8, and similar to the case of a free fiber illustrated in FIG. 4, the largest contribution to the pressure sensitivity of an embedded fiber 30 results from the term e.sub.z.sup.1, which is due to the fiber length change (that is, the first term in Equation 1). However, as illustrated in FIG. 8, as the thickness of the polyurethane layer 60 of an embedded fiber 30 increases, the magnitude of the pressure sensitivity rapidly increases. This rapid increase is primarily due to change resulting from the term e.sub.z.sup.1.
Therefore, as can be seen from FIGS. 4 and 8, the pressure sensitivity of an embedded fiber (FIG. 8) is significantly higher than that of a free fiber (FIG. 4) due to the compliant encapsulant (that is, the polyurethane layer 60 of embedded fiber 30 in FIGS. 5, 6 and 7) which is relatively thick and has low Bulk Modulus. Thus, an embedded fiber would not provide the low pressure sensitivity required for use in a spatially averaging accelerometer sensor.
Pressure Insensitive Fibers
Thus, the pressure sensitivity of an optical fiber is related to the combined effects of pressure induced fiber length changes (resulting from the term e.sub.z.sup.1 in Equation 1) and strain induced index of refraction effect such as the photoelastic effect (resulting from the terms e.sub.r.sup.P and e.sub.z.sup.P in Equation 1). These effects are generally of opposite polarity, as illustrated in FIG. 4. Accordingly, pressure insensitivity can be achieved by balancing these effects.
More specifically, as disclosed in U.S. Pat. No. 4,427,263, it is possible to achieve such balancing by designing fibers consisting of a glass core with a relatively low Bulk Modulus, and a glass substrate surrounding the glass core, wherein the glass substrate has a high Bulk Modulus. The glass core and glass substrate can then be coated with a soft rubber coating, and then with a hard plastic.
Moreover, as disclosed in U.S. Pat. No. 4,427,263, pressure insensitive fibers can be produced by applying a high Bulk Modulus glass substrate or metal coating to conventional fibers. For example, a typical high silica fiber can be made pressure insensitive by coating the fiber with a high Bulk Modulus metal, such as aluminum or nickel.
FIG. 9 is a graph illustrating the calculated sensitivity ##EQU4## of a conventional pressure insensitive fiber as a function of the metal coating thickness of the fiber. More specifically, FIG. 9 illustrates the calculated sensitivity for a fiber coated with nickel and then with a Hytrel (trademark) plastic coating of a 100-.mu.m o.d. As illustrated in FIG. 9, the magnitude of the fiber pressure sensitivity decreases rapidly as the nickel thickness increases and, at approximately 15.5-.mu.m nickel thickness, the fiber becomes pressure insensitive. Therefore, the 15.5-.mu.m nickel thickness of the nickel can be referred to as the "critical thickness." An increase in the Hytrel (trademark) plastic coating thickness results in a further, fairly rapid change in the fiber pressure sensitivity. In this case, the thickness of the nickel must be close to the critical thickness if substantially desensitized fibers are desired.
Generally, fibers are not free, but are mounted on a substrate or are embedded in an encapsulant (as illustrated, for example, in FIGS. 5, 6 and 7). For a fiber embedded in an encapsulant, the pressure sensitivity of the fiber is controlled by the elastic moduli of the encapsulant (such as the polyurethane layer 60 illustrated in FIGS. 5, 6 and 7) surrounding the fiber. Therefore, as illustrated in FIG. 8, a compliant elastomer (such as polyurethane) used as an encapsulant will significantly, and undesireably, increase the fiber pressure sensitivity. This increase in fiber pressure sensitivity is due to the low Bulk Modulus of the compliant elastomer and results primarily from the term e.sub.z.sup.1 corresponding to the direct fiber length change.
Moreover, a conventional pressure insensitive fiber (whether as a free fiber or as an embedded fiber) has relatively good bonding across all layer interfaces. This relatively good bonding has the undesirable effect of efficiently communicating strain to the core of the fiber from surrounding layers. As a result, strain generated in the encapsulant by an applied pressure propagates to the outer coating of the fiber, then to the inner coating, and finally, to the core. This strain causes undesirable phase modulation in light transmitted through the fiber.
Therefore, a conventional pressure insensitive fiber will not be effective when used in a spatially averaging accelerometer sensor due to the pressure sensitivity of the fiber when embedded in an encapsulant.